Multiplication and division of fractions
Last updated: 11 Nov 2008
Now that we know how to find a fraction, even if it is disguised as a decimal or as a percentage, it is time to remind ourselves how to use them.
Multiplication
Multiplication is the easiest of the operations to perform on fractions.
Simply multiply the two numerators (top numbers) to find the resulting numerator, then multiply the two denominators (bottom numbers) to find the new denominator.
Example of Multiplication
Multiply numerators 3 and 2, and denominators 5 and 7, to give .
Division
Division is multiplication by the inverse of the divisor (the second fraction).
First find the inverse (also called the reciprocal) of the fraction.
The inverse can be found by turning the fraction upside down, i.e. swapping the top and bottom numbers. Then multiply as before
Example of Division
Invert to give
And then you can multiply numerators and divisors as before.
Shortcuts
The key to doing well in the math section of the GMAT is to do the minimum amount of work possible, so if there is a shortcut, take it.
Always cancel any common factors from the numerators and denominators before you begin to do any multiplication.
Example of Cancellation
In this case you can cancel the common factor of 3 from the 3 and the 6 before multiplying the two fractions.
